Controlling electric motor cogging

ABSTRACT

A method of determining magnet pole geometry for controlling cogging in an electric motor includes defining the magnet pole geometry in terms of at least one design parameter, predicting cogging as a function of the design parameter, and from the predicted cogging, selecting a value for the design parameter which corresponds to a desired level of cogging in the electric motor.

FIELD OF THE INVENTION

The present invention relates generally to electric motors and, moreparticularly, to controlling cogging in electric motors.

BACKGROUND OF THE INVENTION

Many electromagnetic machines in general, and permanent magnet electricmotors in particular, exhibit torque irregularities as the rotor rotateswith respect to the stator. Such irregularities produce non-uniformtorque output and, thus, non-uniform rotation of the rotor. These torqueirregularities may be caused by the physical construction of a givenmachine. They can result from, for example, a bearing that sticks in agiven rotor position or the fact that, because of the electromagneticcharacteristics of the machine, the rotor tends to prefer certainangular positions with respect to the stator. Torque irregularitiesresulting from the electromagnetic characteristics of a permanent-magnetmachine are commonly known as torque ripple, and the component that ispresent even when the stator windings are not energized is known as“cogging”.

Because cogging is generally undesirable for certain electric motorapplications, including automotive power steering applications,techniques have been explored to reduce cogging. For example,optimization techniques have been applied to identify magnet polegeometries that yield reduced cogging. As recognized by the inventorhereof, however, these known techniques do not predict cogging in anelectric motor as a function of the magnet pole geometry, and thereforedo not facilitate the selection of design parameter values which yield adesired level of cogging in the electric motor.

SUMMARY OF THE INVENTION

The inventor hereof has succeeded at designing a method of determiningmagnet pole geometry for controlling cogging in an electric motor. Themethod includes defining the magnet pole geometry in terms of at leastone design parameter, predicting cogging as a function of the designparameter, and, from the predicted cogging, selecting a value for thedesign parameter which corresponds to a desired level of cogging in theelectric motor.

While some of the principal features and advantages of the inventionhave been described above, a greater and more thorough understanding ofthe invention may be attained by referring to the drawings and thedetailed description of exemplary embodiments which follow.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a flow diagram of a method of determining magnet pole geometryfor controlling cogging in an electric motor according to one embodimentof the present invention.

FIG. 2(a) illustrates an electric motor having a rotor with a magnetpole geometry determined using the method of FIG. 1.

FIG. 2(b) further illustrates the magnet pole geometry of the rotorshown in FIG. 2(a)

FIGS. 3-7 are predicted cogging plots produced for the electric motor ofFIG. 2 using an FEA model.

FIG. 8 is a plot of predicted peak-to-peak cogging produced from thedata of FIGS. 3-7.

FIG. 9 is a block diagram of a power steering device incorporating theelectric motor of FIG. 2.

Corresponding reference characters indicate corresponding featuresthroughout the several views of the drawings.

DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS

A method of determining magnet pole geometry for controlling cogging inan electric motor according to one exemplary embodiment of the presentinvention is illustrated in FIG. 1 and indicated generally by referencenumeral 100. As shown in FIG. 1, the method 100 includes the step 102 ofdefining the magnet pole geometry in terms of at least one designparameter. The method 100 further includes the step 104 of predictingcogging as a function of the design parameter. At step 106, thepredicted cogging is used to select a value for the design parameterwhich corresponds to a desired level of cogging in the electric motor.For example, in the case of an electric motor application in whichcogging is generally undesirable, the predicted cogging can be used toselect a value for the design parameter which corresponds to a minimumor zero cogging value for the electric motor. Alternatively, thepredicted cogging can be used to select a design parameter value whichwill yield a higher cogging value for the electric motor, if desired.

The design parameter referred to in step 102 of FIG. 1 may be anyparameter which defines the magnet pole geometry (i.e., the size and/orshape of the magnet pole), and whose value can be selected or optimizedas desired. Additionally, the magnet pole geometry can be defined interms of multiple design parameters instead of a single designparameter. In such a case, cogging is preferably predicted as a functionof the multiple design parameters, and this predicted cogging is thenused to select values for the design parameters which correspond to adesired level of cogging in the electric motor.

With further reference to step 104 in FIG. 1, cogging is predicted inone embodiment of the invention using a finite elements analysis (FEA)model of the electric motor, although other means for predicting coggingcan be employed. Further, the cogging which is predicted in oneembodiment is peak-to-peak cogging (also referred to as coggingmagnitude), although this is not strictly necessary.

One exemplary implementation of the method 100 shown in FIG. 1 will nowbe described with reference to FIGS. 2-8. This particular implementationis for a 10 pole/12 slot brushless permanent magnet (BPM) motor 200,which is illustrated generally in FIG. 2(a). It should be understood,however, that the method 100 can be applied to other pole/slotcombinations, as well as to other types of electric motors.

As shown in FIG. 2(a), the motor 200 includes a stator 202 and a rotor204 positioned within the stator 202. The rotor 204 includes severalmagnet poles 206-224, with each magnet pole having the same geometry.Alternatively, the rotor 204 can be designed such that two or more ofits magnet poles have a different geometry, but this will increase thecomplexity of the design. As best shown in FIG. 2(b), the geometry ofeach magnet pole 206-224 in this particular embodiment is defined by twodesign parameters, namely, the magnet pole span BetaM, which defines theangular width of each magnet pole, and the magnet decenter radius Rmo,which defines the degree of curvature for each magnet pole.Alternatively (or additionally), the magnet pole geometry can bedefined, e.g., in terms of a polynomial function. FIG. 2(b) alsoillustrates the parameter Rad1, which represents the outside diameter ofthe rotor 204.

In this particular implementation, the cogging of the electric motor 200shown in FIG. 2 will be predicted using a parametric FEA model of themotor 200 as well as predefined potential values for the designparameters BetaM and Rmo. These potential values can be defined asdiscrete values or, more preferably, as value ranges that canrealistically be used for BetaM and Rmo in the given motorconfiguration. For purposes of this example, assume the value of BetaMcan range from 26 to 32 mechanical degrees, and the value of Rmo canrange from 8.225 to 20.225 millimeters. As appreciated by those skilledin the art, the parametric FEA model of the electric motor can beproduced using any suitable FEA software.

Using the FEA model and the defined value ranges for the designparameters BetaM and Rmo, cogging in the electric motor is predicted asa function of the design parameters. In one preferred embodiment,peak-to-peak cogging (i.e., torque as a function of angular position) isfirst predicted and plotted. This is shown generally in FIGS. 3-7, whichare predicted cogging plots for the electric motor for various values ofBetaM and Rmo. Specifically, FIG. 3 illustrates cogging plots using avalue of 26 mechanical degrees for BetaM, and Rmo values of 8.225,12.225, 16.225, and 20.225 millimeters. FIGS. 4-7 illustrate similarplots using the same values for Rmo, and values of 27.5, 29, 30.5 and 32mechanical degrees, respectively, for BetaM.

Using data points from the predicted cogging plots of FIGS. 3-7, coggingin the electric motor can be predicted and plotted as a function of thedesign parameters, as shown in FIG. 8. More specifically, in FIG. 8,peak-to-peak cogging is plotted as a function of the value of BetaM foreach of the four values of Rmo used in FIGS. 3-7.

Having predicted peak-to-peak cogging as a function of the designparameters BetaM and Rmo, values for these design parameters can beselected which correspond to a desired level of cogging in the electricmotor. For example, it can be seen from FIG. 8 that using a BetaM valueof 27 mechanical degrees and an Rmo value of 8.225 mm yields a predictedcogging value of zero. Alternatively, values can be selected for thedesign parameters BetaM and Rmo which correspond to a higher level ofpredicted cogging, if desired.

With further reference to FIG. 7, it should be noted that the predictedcogging plots are generally sinusoidal. Therefore, an equation can bederived to define a relationship between the design parameters whichyields a desired level of cogging in the electric motor, as follows:Cogging=f(parameter1, parameter2, . . . )==f1(parameter1, parameter2, . . . )*sin(f2(parameter1, parameter2, . . .)In the case where zero cogging is desired, the relationship can bereduced as follows:0=sin(f2(parameter1, parameter2, . . . ), or180n=sin(f2(parameter1, parameter2, . . . ), where n is an integerrepresenting a particular zero crossing of the sinusoidal coggingwaveform.Using values of BetaM and Rmo from FIG. 8 which correspond to zerocogging in the electric motor 200 yields the following expression:B _(m)=6n+π(Rmo/Rad1)²−(7π/3)*(Rmo/Rad1)+(5π/3)±1 mechanical degree.

Thus, using the above equation to select the values of BetaM and Rmoresults in a magnet pole geometry for the rotor 204 shown in FIG. 2which yields a minimum or zero peak-to-peak cogging when the rotor 204is included in the electric motor 200 of FIG. 2. As will be appreciatedby those skilled in the art, a higher value of n corresponds to a widermagnet, and thus a higher output torque for the electric motor 200.Thus, where greater torque is desired, 4<n<6, where the maximum possiblevalue of n (for the 10 pole/12 slot motor under discussion) is six.

In one preferred application of the invention, the electric motor 200 ofFIG. 2 is incorporated into a power steering device 800, as showngenerally in FIG. 8. By choosing values for BetaM and Rmo using theequation set forth above, cogging in the electric motor 200 isminimized, rendering it especially desirable for use in the powersteering device 800.

When introducing elements of the present invention or the preferredembodiment(s) thereof, the articles “a”, “an”, “the” and “said” areintended to mean that there are one or more of such elements. The terms“comprising”, “including” and “having” are intended to be inclusive andmean that there may be additional elements other than those listed.

As various changes could be made in the above constructions withoutdeparting from the scope of the invention, it is intended that allmatter contained in the above description or shown in the accompanyingdrawings shall be interpreted as illustrative and not in a limitingsense.

1. A method of determining magnet pole geometry for controlling cogging in an electric motor, the method comprising: defining the magnet pole geometry in terms of at least one design parameter; predicting cogging as a function of the design parameter; and from the predicted cogging, selecting a value for the design parameter which corresponds to a desired level of cogging in the electric motor.
 2. The method of claim 1 wherein predicting cogging includes predicting peak-to-peak cogging.
 3. The method of claim 2 wherein selecting includes selecting a value for the design parameter which corresponds to zero peak-to-peak cogging.
 4. The method of claim 1 wherein predicting includes predicting cogging as a function of the design parameter using an FEA model of the electric motor.
 5. The method of claim 1 wherein defining includes defining the magnet pole geometry in terms of a plurality of design parameters, predicting includes predicting peak-to-peak cogging as a function of the design parameters using an FEA model, and selecting includes selecting values for the design parameters which correspond to a minimum peak-to-peak cogging value for the electric motor.
 6. The method of claim 1 wherein the electric motor includes a plurality of magnet poles, and defining includes defining a same magnet pole geometry for each of the plurality of magnet poles.
 7. The method of claim 1 wherein the design parameter is selected from the group consisting of magnet pole span and magnet decenter radius.
 8. A method of determining magnet pole geometry for an electric motor, the method comprising: defining the magnet pole geometry in terms of a plurality of design parameters; producing a parametric FEA model of the electric motor; predicting peak-to-peak cogging as a function of the design parameters using the FEA model; from the predicted peak-to-peak cogging, selecting values for the design parameters which correspond to a desired level of peak-to-peak cogging in the electric motor.
 9. The method of claim 8 further comprising defining potential values for each of the design parameters.
 10. The method of claim 9 wherein defining includes defining a range of potential values for each of the design parameters.
 11. The method of claim 9 wherein predicting includes predicting peak-to-peak cogging as a function of the design parameters using the FEA model and the defined potential values.
 12. The method of claim 8 wherein selecting includes selecting values for the design parameters which correspond to a minimum peak-to-peak cogging value.
 13. The method of claim 12 wherein selecting includes selecting values for the design parameters which corresponding to zero peak-to-peak cogging.
 14. The method of claim 8 further comprising defining a pole/slot combination for the electric motor.
 15. The method of claim 8 wherein selecting includes using the predicted peak-to-peak cogging to define a relationship between the design parameters which yields a minimum peak-to-peak cogging value, and determining values for the design parameters using the defined relationship.
 16. The method of claim 15 wherein the defined relationship is a periodic function.
 17. The method of claim 16 wherein the defined relationship is a sinusoidal function.
 18. A rotor for an electric motor, the rotor having a diameter and comprising a plurality of permanent magnets, each of the permanent magnets having a magnet decenter radius value Rmo and a magnet pole span value B_(m), wherein: B _(—m)=6n+π(Rmo/Rad1)²−(7π3)*(Rmo/Rad1)+(5π3)±1 mechanical degree, Rad1 is the diameter of the rotor, and n is an integer greater than one.
 19. A rotor according to claim 18 wherein the rotor is configured for a 10 pole/12 slot BPM motor.
 20. A rotor according to claim 18 wherein 4≦n≦6.
 21. An electric motor comprising the rotor of claim
 18. 22. A power steering device comprising the electric motor of claim
 21. 